A line is shown on the graph.
Which choice gives an equation of the line?
A graph with two marked points gives you enough information to find a line’s slope and intercept. Divide the change in by the change in , then put one point into and use a Desmos regression to find . A point’s -value is the intercept only when its -value is . Keep the slope fraction in the right order.
Hints
- Hint 1
A slope compares the change in with the change in . Move from one marked point to the other: how far do you go right, and how far do you go down? Down counts as negative.
- Hint 2
The y-intercept is the height where . Neither marked point has , so neither marked -value is . Put the slope and one marked point into .
- Hint 3
A Desmos regression can find the unknown : type the equation from your point with instead of . Read under PARAMETERS, then match both the slope and intercept to a choice.
Step-by-step
Find the slope, then the intercept
Step 1Read the changes between the marked points
From to , you move units right and units down. Use the marked coordinates, not how steep the line looks.
- Step 2
Find the slope
The slope is the vertical change divided by the horizontal change. Down is negative, so divide the change by the change:
Reduce the fraction:
Don’t flip the fraction: the horizontal change goes on the bottom.
- Step 3
Use a point to find the intercept
The y-intercept is when . The marked point is not on the -axis, so is not . Substitute that point and the slope into :
- Step 4
Solve for the intercept in Desmos
Type . The tells Desmos to fit the unknown ; it shows under PARAMETERS. Since , that’s the line’s intercept.
- Step 5
Match both parts of the equation
In slope-intercept form , the slope multiplies . Match both and :
That’s the equation of the graphed line. Choice A.