Answer:
a) y= 2x
b) 5
c) y= 3x +12
Step-by-step explanation:
a) First, choose 2 points in which the line passes through.
(0, 0) and (2, 4)
We can write the equation of the line in the form of y= mx +c, where m is the gradient and c is the y-intercept. This is also known as the slope-intercept form.
[tex]\boxed{slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Slope of the line
[tex] = \frac{4 - 0}{2 - 0} [/tex]
[tex] = \frac{4}{2} [/tex]
= 2
Substitute m=2 into the equation:
y= 2x +c
Since the y- intercept is at y=0, c= 0.
Thus, the equation of the straight line shown is y= 2x.
_______
b) y= 3x +5
When x= 0,
y= 3(0) +5
y= 5
Thus, y= 3x +5 passes through (0, 5).
_______
c) y= 3x +5
Recall: in the slope- intercept form (y=mx +c), the coefficient of x is the gradient
Thus, the gradient of the given line is 3.
Given that the unknown line has the same gradient as y= 3x +5, its gradient is 3.
Substitute m= 3 into the equation:
y= 3x +c
To find the value of c, substitute a pair of coordinates into the equation.
When x= 0, y= 12,
12= 3(0) +c
12= 0 +c
c= 12
Thus, the equation of the straight line is y= 3x +12.
*Note: gradient and slope has the same meaning and has been used interchangeably.
