Question

A) Write an equation of a line that passes through the point (2, 4) and whose slope is 1/2.
B)Find the equation of a line in slope-intercept from that passes through the points (6,5) and (4,1).
C)Write the equation of the horizontal or vertical line: (-7, 3), slope is undefined.
D)Find the equation of a line perpendicular to the given line: y = 3x – 1.
E)Write an equation in slope-intercept form for an equation of a line perpendicular to y = -3x +1 and that intersects at point (1, 2/3).

Answer 1

a.)use: \[y=mx+b\],where m is the slope,
solve for the value of b using the given coordinates
b.)use the slope formula\[m=\frac{ \Delta y }{ \Delta x }\], then solve for b again

Answer 2

A.) y - y1 = m(x - x1) using slope 1/2 and points (2,4)
y - 4 = 1/2(x - 2)
y - 4 = 1/2x - 1
y = 1/2x - 1 + 4
y = 1/2x + 3

B) find the slope first
slope(m) = (y2 - y1) / (x2 - x1) using points (6,5) and (4,1)
m = (1 - 5) / (4 - 6)
m = -4/-2
m = 2

y - y1 = m(x - x1) using slope 2 and points (6,5)
y - 5 = 2(x - 6)
y - 5 = 2x - 12
y = 2x - 12 + 5
y = 2x - 7

C) It is a vertical line. The equation is y = 3

D) A perpendicular line will have a negative reciprocal of the slope given. The slope given is 3, so the slope you need will be -1/3.
I am sorry I am not sure about this one ....because there is no points given.

E) perpendicular line...negative reciprocal to slope -3 is 1/3.
y - y1 = m(x - x1)
y - 2/3 = 1/3(x - 1)
y - 2/3 = 1/3x - 1/3
y = 1/3x - 1/3 + 2/3
y = 1/3x + 1/3

any questions ?