Step-by-step explanation:
the easiest way (at least for me) is to stay with the point-slope form and then transform it to get the slope-intercept form.
the general slope-intercept form is
y = ax + b
a being the slope, and b the y-intercept (the y-value when x = 0).
the general point-slope form is
y - y1 = a(x - x1)
a is again the slope, and (x1, y1) is a point on the line.
so,
1.
y - 1 = 2(x - 4)
y = 2(x - 4) + 1 = 2x - 8 + 1 = 2x - 7
y = 2x - 7
2.
y - 4 = 1/2 × (x - 2)
y = 1/2 × (x - 2) + 4 = x/2 - 1 + 4 = x/2 + 3
y = 1/2 × x + 3 or x/2 + 3
3.
y - 0 = 2/3 × (x - -6)
y = 2/3 × x + 4 or 2x/3 + 4
4.
y - -1 = -3/4 × (x - -8)
y + 1 = -3/4 × x - 6
y = -3/4 × x - 7 or -3x/4 - 7
5.
y - -3 = -1×(x - 4)
y + 3 = -x + 4
y = -x + 1
6.
y - -9 = 4(x - 0)
y + 9 = 4x
y = 4x - 9
