1. Write the equation of the line which has y-intercept (0, 5) and is perpendicular to the line with equation y = –3x + 1.
You're given the slope of a line y=-3x +1, is obviously -3. Therefore the perpindicular line you are trying to find has slope 1/3. Now you have the slope and a point on the line, use the line formula y-y1=m(x-x1) and rearrange.
y=(1/3)x + 5
2. Write the equation of the line that passes through point (–7, 9) with a slope of –2
Simpler than above, just use the line formula;
y-9=-2x + 7
3. Find the slope and y-intercept.
–2x + 10y = –20
rearrange for and make y the subject, the coefficient of x is the slope and the added constant is the y-coordinate of the y-intercept;
therefore the slope is 1/5 and the y intercept is (0,-4)
remember the key concepts here; the relationship of slopes between perpindicular and parallel lines, how to use the line and slope formulas; and recognising the form y=mx+b in finding slopes and y-intercepts.