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.
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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?
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