Answer:
see attached graph
Step-by-step explanation:
There are a couple of ways you can look at this.
Point-Slope Form
The point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
Comparing this to the given equation, we see that ...
k = -14, m = -7, h = 0
That is, the equation describes a line with slope -7 through point (0, -14).
The slope is the ratio of rise to run. Usually, "run" is considered to be positive in the +x direction (to the right). Here, you run out of room on most graphs if you look for a point that is 7 units down and 1 unit right of the y-intercept at (0, -14). (That point is (1, -21).) So, it is more convenient to start at the y-intercept (0, -14) and go 1 unit left and 7 units up to find another point on the line. That point is (-1, -7). With two points plotted, you can draw the graph.
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Slope-Intercept form
We discovered above that the y-intercept is -14. You can get there also by putting the equation in slope-intercept form:
y = mx +b . . . . . . line with slope m and y-intercept (0, b)
Adding -14 to both sides of the given equation gives you this form.
y = -7x -14
The method of plotting is substantially identical to that described above.
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Standard form
The standard form of the equation is ...
ax +by = c
where a > 0, and a, b, c are mutually prime integers.
Adding 7x-14 to both sides of the equation puts it into standard form:
7x +y = -14
The x- and y-intercepts are found by setting the other variable to zero and solving for the one that is left. Here, that means the x-intercept is ...
c/a = -14/7 = -2
and the y-intercept is ...
c/b = -14/1 = -14
These x- and y-intercepts are easily plotted on the x- and y-axes. The graph will be the line drawn through them. The attached graph shows the line and the intercepts.
