Linear Graph Questions for Class 8: Slope, Intercept, and Plotting Practice

Algebra and Function Practice

Linear graphs connect equations to pictures. A straight line on a coordinate grid shows a constant rate of change. In this lesson you will read slope and intercept from a drawn line, plot a line from its equation, and sketch a line from a short word problem. The convention used here is simple: slope is vertical change divided by horizontal change between two clear grid points, and intercept is where the line crosses the vertical axis. Letter styles and handwriting vary, so answers are judged by correct coordinates, correct direction, and a labeled check point rather than by perfect drawing.

Practice materials: Printable downloads are not available for this lesson yet. Use the instructions and four exercises below.

Reading slope and intercept from a graph

A linear graph is a straight line on a grid with a horizontal axis and a vertical axis. The vertical intercept is the value where the line crosses the vertical axis. The slope measures steepness: it is the vertical change divided by the horizontal change as you move from one point on the line to another.

Choose two points where the line passes exactly through grid intersections. Count the vertical change and the horizontal change. Keep the sign: rising to the right gives a positive slope, falling to the right gives a negative slope. A horizontal line has slope zero. A vertical line is not a function graph in this lesson and is excluded.

Always state units if the axes have labels. If the vertical axis is cost in dollars and the horizontal axis is hours, then slope is dollars per hour. The intercept is the starting cost when hours equal zero.

1. Find where the line crosses the vertical axis and record that value as the intercept.
2. Pick two grid-intersection points on the line and label them with coordinates.
3. Subtract the vertical values and subtract the horizontal values in the same order.
4. Divide vertical change by horizontal change and simplify the fraction.
5. Check by moving from the intercept using the slope and confirming you land on another grid point.

Plotting a line from an equation

An equation in the form y = m x + b gives the slope m and the vertical intercept b directly. Start at b on the vertical axis, then use the slope as a step pattern. For example, slope 2 means up 2 for every 1 right; slope negative one half means down 1 for every 2 right.

Plot at least three points so a mistake is visible. Two points determine a line, but a third point acts as a check. Use simple x values such as 0, 1, and 2, or negative values when the intercept is high. Connect the points with a straight edge and extend the line across the grid.

Label the line with its equation. If the grid is small, choose points that stay inside the visible area. The line does not stop at the last plotted point; arrows or extension to the grid edge show it continues.

1. Write the equation in y = m x + b form and identify m and b.
2. Plot the intercept point on the vertical axis.
3. Use the slope to step to a second point and plot it.
4. Compute a third point by substituting an x value into the equation.
5. Draw a straight line through all three points and label it.

Sketching a linear graph from a word problem

Word problems often describe a starting amount and a constant rate. The starting amount is the intercept, and the rate is the slope. Decide what each axis represents before drawing. Put the independent quantity on the horizontal axis and the dependent quantity on the vertical axis.

For example, a plant is 4 cm tall and grows 2 cm per week. Height depends on weeks, so weeks go on the horizontal axis and height on the vertical axis. The intercept is 4 and the slope is 2. A sketch needs labeled axes, a marked intercept, one more clear point, and a straight line.

Check the sketch by reading one point back into the story. If the line passes through 3 weeks and 10 cm, then 4 plus 2 times 3 equals 10, which matches.

1. Name the independent and dependent quantities and label the axes.
2. Identify the starting value as the intercept.
3. Identify the constant rate as the slope, including units.
4. Plot the intercept and one additional point using the rate.
5. Draw the line and verify one point against the story.

Worked example

A line passes through the points (0, 3) and (4, 11). Find the slope and intercept, then write the equation.

Four practice exercises

Common mistakes

• Counting slope as horizontal change over vertical change. Slope is vertical change divided by horizontal change. Write the fraction with the vertical number on top before simplifying.
• Ignoring the sign of the slope when the line falls to the right. A falling line has a negative slope. Check that your vertical change is negative when the horizontal change is positive.
• Plotting only two points and drawing a line through a plotting error. Plot a third point from the equation. If the three points do not line up, recheck the arithmetic.
• Swapping the axes in a word problem. Ask which quantity depends on the other. The dependent quantity goes on the vertical axis.

Self-check rubric

• Intercept is read correctly from the vertical axis and stated as a single value.
• Slope is computed as vertical change divided by horizontal change with the correct sign.
• Equation is written in y = m x + b form with m and b matching the graph.
• Plotted line passes through at least three correct grid-intersection points.
• Axes are labeled and the line is labeled with its equation.
• Word-problem sketch identifies independent and dependent quantities correctly.
• Check point is stated and verified by substitution or by reading the graph.
• Valid alternative conventions are accepted if coordinates, direction, and labels are correct.

Questions and answers