# Equation of a line

I've been practising some past previous exam question and came across this:

How would you find the equation of the line with y-intercept? -$\frac{3}{4}$ and slope -$\frac{1}{2}$?

• I love the tags – user137794 Apr 15 '14 at 23:44

So long as the line isn't parallel with the $y$-axis, a general equation for a line is as follows:

$$y = mx + b$$

where $m$ is the slope and $b$ the $y$-intercept.

Draw the following lines: $2x+3, -\frac{1}{2}x+2,3x-5$

From their graphs find their y-intercepts, and slopes.

Try to notice a relationship between the slopes, intercept and the equation of the line

Try to explain this relationship (prove it)

If you find difficulties explaining/proving this relationship, please make another post about what you attempted to prove/explain and I will help.

If you're finding this problem tricky it might be easier to draw a small sketch. If you have no squared paper you can draw eight or ten squares onto blank paper yourself.

If the line crosses the y axis at -3/4 you already have the equation for x = 0, your first point, and if you use the squares to carefully draw a short section of slope with the angle that's indicated in the problem, you'll get a visual intuition and a better sense for the problem before diving straight into the general terms for a solution. Then mark yourself a second point somewhere helpful and simple like x = 1 or x = 2, and only then go back into the algebra to bring it together.

$$y=mx+b\text{ for a non-vertical straight line. Here,}\\ \text{b is the y-intercept, and m is the slope. Hence, the equation is:}\\ \boxed{y=-\dfrac{1}{2}x-\dfrac{3}{4}}$$