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:
\(y = \frac{8}{7}x + \frac{3}{7}\)
What is the slope-intercept form of the equation of the line that contains the points (−3,−3)
and (4, 5)
?
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