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Question
a. Sam knows that the x-intercept of a linear equation is 2 and that the y-intercept is 5. Graph this line on the coordinate plane.
b. Look at the graph and find the slope.
c. Write an equation of the line in slope-intercept form.
d. Use the x-intercept and the slope to write an equation in point-slope for the line.
e. Solve the equation in part d for y. Do you get the same equation that you had in part c? Will this always work? Why or why not?
Scribble
a. The line passes through the points (2,0) and (0,5).
b. The slope of the line can be calculated as (5-0)/(0-2) = 5/-2 = -5/2.
c. The equation of the line in slope-intercept form is y = -5/2x + 5.
d. Using the point-slope form, the equation of the line is y - 5 = -5/2(x - 2).
e. Solving the equation in part d for y, we get y = -5/2x + 5. This is the same equation as in part c. This will always work because both the slope-intercept form and point-slope form represent the same line with the same slope and intercepts.