Question

graph each equation.
$y = \dfrac{7}{4}x - 4$
slope:
y - intercept:

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.

Step2: Identify slope from the equation

Given the equation \(y=\frac{7}{4}x - 4\), comparing it with \(y = mx + b\), we can see that the coefficient of \(x\) is \(\frac{7}{4}\). So, the slope \(m=\frac{7}{4}\).

Step3: Identify y - intercept from the equation

Again, comparing \(y=\frac{7}{4}x - 4\) with \(y = mx + b\), the constant term \(b=- 4\). So, the \(y\) - intercept is \(-4\).

To graph the line:

1. Start by plotting the \(y\) - intercept. The \(y\) - intercept is \(-4\), so we plot the point \((0,-4)\) on the \(y\) - axis.
2. Use the slope to find another point. The slope is \(\frac{7}{4}\), which means for a run of \(4\) (moving \(4\) units to the right along the \(x\) - axis), we have a rise of \(7\) (moving \(7\) units up along the \(y\) - axis). From the point \((0,-4)\), moving \(4\) units to the right (to \(x = 4\)) and \(7\) units up (to \(y=-4 + 7=3\)) gives us the point \((4,3)\).
3. Draw a straight line through the points \((0,-4)\) and \((4,3)\).

Answer:

Slope: \(\frac{7}{4}\)
y - intercept: \(-4\)
(For graphing: Plot \((0, - 4)\) and \((4,3)\) and draw a line through them)