What is the equation of the line that passes through the point $(-4,-3)$ and has a slope of $-\frac{3}{4}$ ?
Answer
\(\boxed{The equation of the line is y = -\frac{3}{4}x - 6}\).
Step 1 ：The equation of a line in slope-intercept form is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. We know the slope \(m\) and a point \((x_1, y_1)\) on the line. We can substitute these values into the equation to solve for \(b\).
Step 2 ：Substitute the given values into the equation: \(-3 = -\frac{3}{4}*(-4) + b\).
Step 3 ：Solve the equation to find the y-intercept \(b\): \(b = -6.0\).
Step 4 ：Now that we have the y-intercept, we can write the equation of the line in slope-intercept form.
Step 5 ：\(\boxed{The equation of the line is y = -\frac{3}{4}x - 6}\).
