Answer :
To find the equation of the line in slope-intercept form, [tex]\( y = mx + b \)[/tex], given the slope and a point on the line, we can follow these steps:
1. Identify the slope [tex]\( m \)[/tex] and the given point [tex]\((x_1, y_1)\)[/tex]:
- Slope [tex]\( m = 4 \)[/tex]
- Given point [tex]\( (x_1, y_1) = (-4, 3) \)[/tex]
2. Use the point-slope form of the equation of a line, which is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Plug in the known values:
[tex]\[ y - 3 = 4(x + 4) \][/tex]
3. Simplify the equation to get it into the slope-intercept form [tex]\( y = mx + b \)[/tex]:
By distributing the slope and solving for [tex]\( y \)[/tex]:
[tex]\[ y - 3 = 4(x + 4) \][/tex]
[tex]\[ y - 3 = 4x + 16 \][/tex]
[tex]\[ y = 4x + 16 + 3 \][/tex]
[tex]\[ y = 4x + 19 \][/tex]
4. Determine the y-intercept [tex]\( b \)[/tex]:
In this case, after simplification, we see that [tex]\( b = 19 \)[/tex].
Therefore, the equation of the line in slope-intercept form is:
[tex]\[ y = 4x + 19 \][/tex]
1. Identify the slope [tex]\( m \)[/tex] and the given point [tex]\((x_1, y_1)\)[/tex]:
- Slope [tex]\( m = 4 \)[/tex]
- Given point [tex]\( (x_1, y_1) = (-4, 3) \)[/tex]
2. Use the point-slope form of the equation of a line, which is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Plug in the known values:
[tex]\[ y - 3 = 4(x + 4) \][/tex]
3. Simplify the equation to get it into the slope-intercept form [tex]\( y = mx + b \)[/tex]:
By distributing the slope and solving for [tex]\( y \)[/tex]:
[tex]\[ y - 3 = 4(x + 4) \][/tex]
[tex]\[ y - 3 = 4x + 16 \][/tex]
[tex]\[ y = 4x + 16 + 3 \][/tex]
[tex]\[ y = 4x + 19 \][/tex]
4. Determine the y-intercept [tex]\( b \)[/tex]:
In this case, after simplification, we see that [tex]\( b = 19 \)[/tex].
Therefore, the equation of the line in slope-intercept form is:
[tex]\[ y = 4x + 19 \][/tex]
