Part 1: The equation of the line is [tex]y=2x+1[/tex]
Part 2: The equation of the line in slope intercept form is [tex]y=-3x-1[/tex]
Explanation:
Part 1: It is given that the point A is [tex](1,3)[/tex] and the line B is [tex]y=2 x-2[/tex]
To determine the line passing through the point A and parallel to line B, let us first determine the slope and y-intercept.
From the equation of line B, the slope is [tex]m=2[/tex]
Substituting the point [tex](1,3)[/tex] and [tex]m=2[/tex] in slope intercept form [tex]y=mx+b[/tex], we have,
[tex]3=2(1)+b[/tex]
[tex]3=2+b[/tex]
[tex]1=b[/tex]
Thus, the y-intercept is [tex]b=1[/tex]
Let us substitute the values [tex]m=2[/tex] and [tex]b=1[/tex] in the slope intercept form [tex]y=mx+b[/tex], we get,
[tex]y=2x+1[/tex]
Thus, the equation of the line passing though point A and parallel to line B is [tex]y=2x+1[/tex]
Part 2: The given two coordinates are [tex](-1,2)[/tex] and [tex](1,-4)[/tex]
To determine the equation of line in slope intercept form, first we shall find the slope and y-intercept.
From the graph, we can see that the line touches the y-axis at -1.
Hence, the y-intercept is [tex]b=-1[/tex]
The formula for slope is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Substituting the coordinates [tex](-1,2)[/tex] and [tex](1,-4)[/tex], we have,
[tex]m=\frac{-4-2}{1+1} =\frac{-6}{2} =-3[/tex]
Thus, the slope is [tex]m=-3[/tex]
Substituting the values [tex]b=-1[/tex] and [tex]m=-3[/tex] in the slope intercept formula [tex]y=mx+b[/tex], we get,
[tex]y=-3x-1[/tex]
Thus, the equation of the line in slope intercept form is [tex]y=-3x-1[/tex]
