Question

The line (y=kx+5) goes through the point (-6,14). graph the line (with points and pictures please!)

Answer 1

y = -1.5x + 5

Explanation:

Using two points, we can solve for the slope of a line.

Slope-Intercept Form

The question describes the line y=kx+5. This line is in slope-intercept form. The general formula for slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. As you can see, y=kx+5 is in the same form, but the slope has been replaced with k, and 5 has been plugged in for b. So, to get the find equation of the line, we just need to find k. This means we need to solve for slope.

Slope Formula

Slope is described as rise over run. Slope represents the change in y divided by the change in x.

The formula for finding slope is
`\displaystyle (y_(2)- y_(1) )/(x_(2)- x_(1) )`. This formula requires 2 points; however, only one point is directly stated in the question. Nevertheless, we can find the second point through the y-intercept. The y-intercept is the y-value of the graph when x = 0. So, if the y-intercept is 5, then (0,5) must be a point on the graph. Now, we can use points (-6,14) and (0,5) to find the slope.

• 
  `(14-5)/(-6-0)` =
  `-(9)/(6)` =
  `-(3)/(2)`

This shows that the slope is -3/2 or -1.5. This shows that the graph decreases by 3 as it increases by 2 and vice versa.

Graphing the Line

Now that we have the slope, we can plug it back into the equation to get our final answer.

• y = -1.5x + 5

Then, on a graph plot the points (-6,14) and (0,5). The graph of this equation is the straight line that connects these 2 points. If needed, you can plot additional points by counting 3 units up and 2 units left from an existing point.