Question

writing equations of linear functions
to write the equation of a linear function, we need to know the rate of change, or slope. once we have these values, we can write equations for linear relationships in slope-intercept form, or point-slope form.
if given the slope and an ordered pair of a linear relationship, follow the steps below:
equations from a point and slope

• label x and y in the point-slope formula
• substitute all values into point-slope
• solve the equation for y
• write the equation in slope-intercept form.

in 1-4, the slope and a point on the graph of a linear function are given. write the equation of the line in slope-intercept form

1. slope = $\frac{1}{3}$; (0, 14)
2. slope = -5; (5, -23)
3. slope = 1.75; (10, 16.5)
4. slope = $\frac{2}{5}$; (-15, -8)
5. a line has a slope of -7 and passes through the point (0, -7). is it possible to write the equation of the line without doing any work? explain why or why not.

Explanation:

Answer:

1. $y = \frac{1}{3}x + 14$
2. $y = -5x + 3$
3. $y = 1.75x - 1$
4. $y = \frac{2}{5}x - 2$
5. Yes, because the point $(0, -7)$ is the y-intercept ($b = -7$). Since the slope $m = -7$ is also given, the equation $y = -7x - 7$ can be written directly using the slope-intercept form $y = mx + b$.