Question

Graphs and equations of lines

Answer 1

Answer:

a) $y = -\frac{3}{4} x + 5$

b) $y = 6x-18$

c) $y = \frac{4}{5} x+\frac{19}{5}$

Step-by-step explanation:

a) The slope / gradient is the coefficient of $x$, so for a) it will be $y=-\frac{3}{4} x + C$.

C is the y-intercept, so the full equation will be $y = -\frac{3}{4} x + 5$.

b) Again, since the slope is 6, we know the coefficient of $x$ will be 6.

Now, we have a point on the line and so far, we know the equation is $y=6x+c$. 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.

$-6 = 6(2)+C$

$-6 = 12+C$

$C = -18$

$y = 6x-18$

c) To find the gradient we must use the formula $\frac{rise}{run}$.

rise = change in y value

run = change in x value

so, the gradient $= \frac{7-3}{4-(-1)} = \frac{4}{5}$

Now the equation is $y = \frac{4}{5} x +C$

Again, to find C we substitute any of the coordinates into the equation. I will use (-1,3).

$3 = \frac{4}{5} (-1) +C$

$3 + \frac{4}{5} =C$

$C =\frac{19}{5}$

so c) is $y = \frac{4}{5} x+\frac{19}{5}$