Answer:
a) [tex]y = -\frac{3}{4} x + 5[/tex]
b) [tex]y = 6x-18[/tex]
c) [tex]y = \frac{4}{5} x+\frac{19}{5}[/tex]
Step-by-step explanation:
a) The slope / gradient is the coefficient of [tex]x[/tex], so for a) it will be [tex]y=-\frac{3}{4} x + C[/tex].
C is the y-intercept, so the full equation will be [tex]y = -\frac{3}{4} x + 5[/tex].
b) Again, since the slope is 6, we know the coefficient of [tex]x[/tex] will be 6.
Now, we have a point on the line and so far, we know the equation is [tex]y=6x+c[/tex]. The coordinates of the point are (2,-6). So now we substitute the y and x values into the equation in order to find C.
[tex]-6 = 6(2)+C[/tex]
[tex]-6 = 12+C[/tex]
[tex]C = -18[/tex]
[tex]y = 6x-18[/tex]
c) To find the gradient we must use the formula [tex]\frac{rise}{run}[/tex].
rise = change in y value
run = change in x value
so, the gradient [tex]= \frac{7-3}{4-(-1)} = \frac{4}{5}[/tex]
Now the equation is [tex]y = \frac{4}{5} x +C[/tex]
Again, to find C we substitute any of the coordinates into the equation. I will use (-1,3).
[tex]3 = \frac{4}{5} (-1) +C[/tex]
[tex]3 + \frac{4}{5} =C[/tex]
[tex]C =\frac{19}{5}[/tex]
so c) is [tex]y = \frac{4}{5} x+\frac{19}{5}[/tex]
