What is the slope-intercept form of the equation of the line that contains the points (−3,−3)

Question

and (4, 5)
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Answer 1

To find the slope-intercept form of the equation of a line, we first need to find the slope of the line using the formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Using the points (-3, -3) and (4, 5), we have:

$m=\frac{5-(-3)}{4-(-3)}=\frac{8}{7}$

Now, we can use the slope-intercept form of a line:

$y=mx+b$

where $m$ is the slope and $b$ is the y-intercept.

We can use one of the points (-3, -3) to find b:

$-3=\frac{8}{7}\cdot (-3)+b$

$-3=-\frac{24}{7}+b$

To solve for b, we can add $\frac{24}{7}$ to both sides:

$-3+\frac{24}{7}=b$

$-\frac{21}{7}+\frac{24}{7}=b$

$\frac{3}{7}=b$

Therefore, the equation of the line in slope-intercept form is:

$y=\frac{8}{7}x+\frac{3}{7}$