most ways use finding 2 points and drawing a line through them
one way is subsitution
so when x=0, y=5
when x=1, y=-2
so graph the points (0,5) and (1,-2) and draw a line through them
another way is using the slope and y intercept
y=mx+b
m=slope
b=y intercept
so given
y=-7x+5
y intercept is 5
means that the graph goes through the y axis at y=5
so put a point 5 units above the origin on the y axis
now the slope is -7
so slope is rise/run
-7=-7/1
go up -7 units (aka down 7 units) and 1 unit to the right and put another point there
2 points there now so draw a line through them
another way is the intercept method
find where the graph goes through the x and y axisies
so
where the graph goes through the x axis, y=0, where the graph goes through the y axis, x=0
so
solve for when x=0 and when y=0
when x=0, y=5
when y=0, x=5/7
so y intercept is 5
x intercept is 5/7
y intercept: go 5 units up from the origin and draw a point there
x intercept: go 5/7 units to the right of the origin and draw point there
connect the 2 points
done
these are 3 ways to graph that equation