Question

A system of linear equations is shown on the graph. The equation of one of the lines is y = 1/2x + 4

Answer 1

Answer:

$y = 3x - 1$

Step-by-step Explanation:

From the graph given, let's label the lines as line A and line B. As indicated in the attachment below.

The equation of a line is given as y = mx + b

Where, m is the slope, which is:

$m = \frac{y2 - y1}{x2 - x1}$

b is the y-intercept. It is the point at which the line crosses or intercepts the y-axis. At this point, x = 0.

Having known this, let's figure out which of the lines has the equation, y = ½x + 4

From the equation given, it means the line's m = ½, and it's y-intercept (b), where the line intercepts the y-axis = 4.

Taking a look at line A and B that we've labelled in the attachment below, line A intercepts the y-axis at 4. This means value of b for line A = 4.

If we calculate the slope (m) for line A using the points labelled in the attachment below, we would arrive at ½ as the slope (m) of line A.

Therefore, the equation y = ½x + 4 is for line A.

Let's find the equation for line B.

=>Find the slope (m) of line B using any 2 coordinate pairs of line B.

We're using the 2 coordinates points, (0, -1), (-1, -4) as indicated in the attachment below.

$m = \frac{y2 - y1}{x2 - x1}$

$m = \frac{-4 - (-1)}{-1 - 0}$

$m = \frac{-4 + 1)}{-1}$

$m = \frac{-3)}{-1}$

$m = 3$

Line B intercepts the y-axis at -1. Therefore, the y-intercept (b) for line B = -1

The equation for line B would be:

$y = 3x - 1$