Slope-intercept equation from graph - Question

Answers

1. \(y=-\frac{3}{2} x+3\).

We are asked to complete the equation in slope-intercept form: \(y=m \cdot x+b\). In this form, \(m\) gives us the slope of the line and \(b\) gives us its \(y\)-intercept.

By looking at the graph, we can see that the \(y\)-intercept is \((0,3)\).

In order to find the slope, we need another point on the line whose coordinates are clearly visible. Such a point is \((2,0)\).


Now, to find the slope, we need to take the ratio of the corresponding differences in the \(y\)-values and the \(x\)-values:

\(\frac{0-3}{2-0}=\frac{-3}{2}=-\frac{3}{2}\)

The equation is \(y=-\frac{3}{2} x+3\).


2. \(y=2 x+4\).

We are asked to complete the equation in slope-intercept form: \(y=m \cdot x+b\). In this form, \(m\) gives us the slope of the line and \(b\) gives us its \(y\)-intercept.

By looking at the graph, we can see that the \(y\)-intercept is \((0,4)\).

In order to find the slope, we need another point on the line whose coordinates are clearly visible. Such a point is \( (1,6)\).

Now, to find the slope, we need to take the ratio of the corresponding differences in the \(y\)-values and the \(x\)-values:

\(\frac{6-4}{1-0}=\frac{2}{1}=2\)

The equation is \(y=2 x+4\).


3. \(y=\frac{3}{4} x-2\).

We are asked to complete the equation in slope-intercept form: \(y=m \cdot x+b\). In this form, \(m\) gives us the slope of the line and \(b\) gives us its \(y\)-intercept.

By looking at the graph, we can see that the \(y\)-intercept is \((4,1)\).


Now, to find the slope, we need to take the ratio of the corresponding differences in the \(y\)-values and the \(x\)-values:

\(\frac{1-(-2)}{4-0}=\frac{3}{4}\)

The equation is \(y=\frac{3}{4} x-2\).


4. \(y=x-5\).

We are asked to complete the equation in slope-intercept form: \(y=m \cdot x+b\). In this form, \(m\) gives us the slope of the line and \(b\) gives us its \(y\)-intercept.

By looking at the graph, we can see that the \(y\)-intercept is \((1,-4)\).

In order to find the slope, we need another point on the line whose coordinates are clearly visible. Such a point is \( (1,-4)\).

Now, to find the slope, we need to take the ratio of the corresponding differences in the \(y\)-values and the \(x\)-values:

\(\frac{-4-(-5)}{1-0}=\frac{1}{1}=1\)

The equation is \(y=x-5\).