Question

y = \frac{7}{4}x - 3\
y = x\
click to select points on the graph.

Explanation:

Step1: Find intersection point

Set $\frac{7}{4}x - 3 = x$
Subtract $x$ from both sides: $\frac{7}{4}x - x - 3 = 0$
Simplify: $\frac{3}{4}x - 3 = 0$
Solve for $x$: $\frac{3}{4}x = 3 \implies x = 4$
Substitute $x=4$ into $y=x$: $y=4$
Intersection point: $(4, 4)$

Step2: Find points for $y=x$

Choose $x=0$: $y=0$, point $(0,0)$
Choose $x=-4$: $y=-4$, point $(-4,-4)$

Step3: Find points for $y=\frac{7}{4}x-3$

Choose $x=0$: $y=-3$, point $(0,-3)$
Choose $x=8$: $y=\frac{7}{4}(8)-3=14-3=11$, point $(8,11)$
Choose $x=-4$: $y=\frac{7}{4}(-4)-3=-7-3=-10$, point $(-4,-10)$

Answer:

For $y=x$: Plot points $(0,0)$, $(-4,-4)$, $(4,4)$ and draw a straight line through them.
For $y=\frac{7}{4}x-3$: Plot points $(0,-3)$, $(-4,-10)$, $(4,4)$ and draw a straight line through them.
The lines intersect at $(4, 4)$.