Answer:
1) (6, 0), (0, 3)
2) -½
3) y= -½x +3
4) -½
5) 2
Step-by-step explanation:
1) x- intercept is the point at which the line passes though the x-axis.
From the graph, the x- intercept is (6, 0).
The y-intercept is the point at which the line passes through the y- axis.
From the graph, the y-intercept is (0, 3).
2) To find the slope, plug in the coordinates of any two points on the line into the gradient formula below.
[tex]\boxed{slope = \frac{y1 - y2}{x1 - x2} }[/tex]
I will use the 2 points that they have provided to calculate the slope.
[tex]slope = \frac{5 - ( - 2)}{ - 4 - 10} [/tex]
[tex]slope = \frac{7}{ - 14} [/tex]
[tex]slope = - \frac{1}{2} [/tex]
3) The equation of a line can be written as y= mx +c, where m is the gradient and c is the y-intercept.
Since we have already found those values in the previous questions, let's substitute them into the equation.
[tex]y = - \frac{1 }{2} x + 3[/tex]
4) Parallel lines have the same slope.
Thus, the slope of a line parallel to the line in the graph will also have a slope of -½.
5) The product of the gradients of perpendicular lines is -1.
(gradient of perpendicular line)(-½)= -1
Gradient of perpendicular line
[tex] = - 1 \div - \frac{1}{2} [/tex]
= 2
