Answer :
To find the equation of the line that has a slope of 2 and passes through the point (2, 4), we will use the point-slope form of the equation of a line. The point-slope form is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\( m \)[/tex] is the slope of the line, and [tex]\((x_1, y_1)\)[/tex] is a point on the line.
Given:
- The slope [tex]\( m = 2 \)[/tex]
- The point [tex]\((x_1, y_1) = (2, 4)\)[/tex]
Substitute the given values into the point-slope form:
[tex]\[ y - 4 = 2(x - 2) \][/tex]
Now, simplify the equation to get it into the slope-intercept form [tex]\(y = mx + b\)[/tex]:
1. Distribute the slope 2 on the right-hand side of the equation:
[tex]\[ y - 4 = 2x - 4 \][/tex]
2. Add 4 to both sides of the equation to isolate [tex]\( y \)[/tex]:
[tex]\[ y - 4 + 4 = 2x - 4 + 4 \][/tex]
[tex]\[ y = 2x \][/tex]
So, the equation of the line is:
[tex]\[ \boxed{y = 2x} \][/tex]
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\( m \)[/tex] is the slope of the line, and [tex]\((x_1, y_1)\)[/tex] is a point on the line.
Given:
- The slope [tex]\( m = 2 \)[/tex]
- The point [tex]\((x_1, y_1) = (2, 4)\)[/tex]
Substitute the given values into the point-slope form:
[tex]\[ y - 4 = 2(x - 2) \][/tex]
Now, simplify the equation to get it into the slope-intercept form [tex]\(y = mx + b\)[/tex]:
1. Distribute the slope 2 on the right-hand side of the equation:
[tex]\[ y - 4 = 2x - 4 \][/tex]
2. Add 4 to both sides of the equation to isolate [tex]\( y \)[/tex]:
[tex]\[ y - 4 + 4 = 2x - 4 + 4 \][/tex]
[tex]\[ y = 2x \][/tex]
So, the equation of the line is:
[tex]\[ \boxed{y = 2x} \][/tex]
