Find the equation of the line that passes through the point (4, -2) and has a y-intercept of 3.
Answer
Step 3: Substitute \(m = -\frac{5}{4}\) and \(b = 3\) back into the equation \(y = mx + b\) to get the final equation of the line: \(y = -\frac{5}{4}x + 3\)
Step 1 ：Step 1: Recall that the equation of a line in slope-intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Step 2 ：Step 2: We already know the y-intercept \(b = 3\). To find the slope, we use the formula \(m = \frac{y - b}{x}\), substituting the given point (4, -2) into the equation: \(m = \frac{-2 - 3}{4} = -\frac{5}{4}\)
Step 3 ：Step 3: Substitute \(m = -\frac{5}{4}\) and \(b = 3\) back into the equation \(y = mx + b\) to get the final equation of the line: \(y = -\frac{5}{4}x + 3\)
