Question

Please show me how to determine the equation of the straight line, with all the steps explained

Answer 1

The equation of a line is usually written in the form of y=mx+c, where m is the gradient and c is the y-intercept. I'll be using question a to explain how to find the equation of a straight line graph.

To find the equation of a line, you would need:

① Gradient

② A coordinate

Let's identify the two coordinates given first.

They are (0,3) and (-3,0)

To find the gradient, use the formula below.

`gradient = (y1 - y2)/(x1 - x2)`

Thus, gradient of line

`= (3 - 0)/(0 - ( - 3)) \\ = (3)/(3) \\ = 1`

Subst. m=1 into the equation:

y= x +c

If the y-intercept is not given, you can substitute a coordinate into the equation to find the value of c.

However, it is already given for this question and you can see that the y-intercept occurs at y=3. Thus, c=3.

Hence, the equation of the line is y= x +3.