Answer:So, the slope-intercept form of the equation for the line through the point (4, -2) with a slope of \(3/4\) is \(y = \frac{3}{4}x - 5\).
Step-by-step explanation:The slope-intercept form of a linear equation is given by \(y = mx + b\), where \(m\) is the slope, and \(b\) is the y-intercept.
Given the point (4, -2) and a slope of \(3/4\), substitute these values into the equation:
\[y = mx + b\]
\[y = \frac{3}{4}x + b\]
Now, use the given point (4, -2) to solve for \(b\):
\[-2 = \frac{3}{4}(4) + b\]
\[-2 = 3 + b\]
\[b = -5\]
Now that we have the values for \(m\) and \(b\), the equation of the line is:
\[y = \frac{3}{4}x - 5\]
So, the slope-intercept form of the equation for the line through the point (4, -2) with a slope of \(3/4\) is \(y = \frac{3}{4}x - 5\).
