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The equation of line 
f is 
y-7=(3)/(10)(x-4). Line 9 , which is parallel to line 
f, includes the point 
(10,4). What is the equation of line 
g ?

The equation of line f f is y7=310(x4) y-7=\frac{3}{10}(x-4) . Line 99 , which is parallel to line f f , includes the point (10,4) (10,4) . What is the equation of line g g ?

Full solution

Q. The equation of line f f is y7=310(x4) y-7=\frac{3}{10}(x-4) . Line 99 , which is parallel to line f f , includes the point (10,4) (10,4) . What is the equation of line g g ?
  1. Understand relationship between parallel lines: Understand the relationship between parallel lines.\newlineDo parallel lines have the same slope?\newlineYes, parallel lines have the same slope.
  2. Determine slope of line ff: Determine the slope of line ff. The equation of line ff is given in point-slope form: y7=310(x4)y - 7 = \frac{3}{10}(x - 4). The slope of line ff is the coefficient of (x4)(x - 4), which is 310\frac{3}{10}.
  3. Line gg parallel to line ff: Since line gg is parallel to line ff, it must have the same slope. The slope of line gg is therefore also 310\frac{3}{10}.
  4. Write equation of line g: Use the point (10,4)(10, 4) and the slope 310\frac{3}{10} to write the equation of line g in point-slope form.\newlineStart with the point-slope form equation: yy1=m(xx1)y - y_1 = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is the point the line passes through.\newlinePlug in the slope 310\frac{3}{10} and the point (10,4)(10, 4): y4=310(x10)y - 4 = \frac{3}{10}(x - 10).
  5. Convert to slope-intercept form: Convert the point-slope form equation to slope-intercept form y=mx+by = mx + b.\newliney4=310(x10)y - 4 = \frac{3}{10}(x - 10)\newliney=310x31010+4y = \frac{3}{10}x - \frac{3}{10}\cdot10 + 4\newliney=310x3+4y = \frac{3}{10}x - 3 + 4\newliney=310x+1y = \frac{3}{10}x + 1

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