Q. The equation of line f is y−7=103(x−4). Line 9 , which is parallel to line f, includes the point (10,4). What is the equation of line g ?
Understand relationship between parallel lines: Understand the relationship between parallel lines.Do parallel lines have the same slope?Yes, parallel lines have the same slope.
Determine slope of line f: Determine the slope of line f. The equation of line f is given in point-slope form: y−7=103(x−4). The slope of line f is the coefficient of (x−4), which is 103.
Line g parallel to line f: Since line g is parallel to line f, it must have the same slope. The slope of line g is therefore also 103.
Write equation of line g: Use the point (10,4) and the slope 103 to write the equation of line g in point-slope form.Start with the point-slope form equation: y−y1=m(x−x1), where m is the slope and (x1,y1) is the point the line passes through.Plug in the slope 103 and the point (10,4): y−4=103(x−10).
Convert to slope-intercept form: Convert the point-slope form equation to slope-intercept formy=mx+b.y−4=103(x−10)y=103x−103⋅10+4y=103x−3+4y=103x+1
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