Question

Graph the line y=−5/4x−3.

Use the line tool and select two points on the line.

Answer 1

To graph a linear function, we can find and graph coordinate points.

Zeros

First, we can find the zeros of the graph. The zeros of a function are where the line intersects with the x-axis, aka when y = 0. To find the zeros of a function, set y equal to 0 and solve for x.

• 
  `0 = -(5)/(4)x-3`
• x = -2.4

Since there is a zero at x = -2.4, we know that one point of the graph will be (-2.4, 0).

Y-intercept

Next, we can use the y-intercept. The y-intercept of a function is where the line intersects with the y-axis, aka when x = 0. To find the y-intercept we can set x equal to 0 and solve for y. However, we don't have to do that for linear functions. Linear functions are written as y = mx + b, where m is the slope and b is the y-intercept. So, from just looking at the equation, we can tell that the y-intercept is -3.

Thus, (0, -3) will be a point on the graph.

Slope

Finally, we can use the slope to find another point. Slope is the change in y over the change in x. Based on the slope of
`-(5)/(4)`, we know that the graph goes down by 5 and right by 4. Since we know this, we can find the point that is 5 down and 4 right from another point, such as (0, -3).

• (0 + 4, -3 - 5) = (4, -8)

This means that (4, -8) will be a point.

Graphing

Now that we have 3 coordinate points, we can graph these points and connect them with a straight line.