Question

What is the equation of the line in slope-intercept form?

Answer 1

`y=(3)/(5)x+3`

Explanation:

Slope-intercept form is the most common form of a linear function.

Formula

The formula for slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. In this question, we must find both m and b by looking at a graph.

Slope

The slope is the change in y over the change in x. So, one way to find the slope is to identify 2 points on the graph and count the difference between them.

• For example, the points (-5,0) and (0,3). First, the y-value increases by 3. Then, the x-value increases by 5. This gives us the final slope,
  `\displaystyle(3)/(5)`.

Another way to find the slope is to use the formula
`\displaystyle(y_(2)- y_(1) )/(x_(2)- x_(1) )`. You can plug in the values from both points and solve to get the same answer.

Y-Intercept

The y-intercept is easy to find from a graph. The y-intercept is wherever the line intersects with the y-axis (the vertical axis). In this case, the line intersects at y-value 3. So, 3 is the b-value in the equation.

Final Equation

Using the information above, we can say that the equation of the line in slop-intercept form is
`y=(3)/(5)x+3`.